Solving cot²x + cosec²x = 7 and cosec²(2x) + cot(2x) = 3

[ibysaiyan]

Homework Statement

this time i have posted two questions on a post, instead of me creating posts all over the forum.

a)cot^2x + cosec^2x = 7
b) (2 cosec^2)2x + cot2x =3
find out the solutions.

Homework Equations

cosec^2 = 1+ cot^2

The Attempt at a Solution

a) cot^2x + cosec^2x = 7
cosec^2-1 + cosec^2 = 7
2cosec^2x = 8
now i thought of solving it by the difference of squares?
couldn't solve it =/
b) totally cluesless as this one has 2 after function cot i.e cot2x =/

 

[Mark44]

Homework Statement

this time i have posted two questions on a post, instead of me creating posts all over the forum.

a)cot^2x + cosec^2x = 7
b) (2 cosec^2)2x + cot2x =3

It's not very clear what the equation above is saying. You are at least using parentheses, but not in the most helpful way.
Is this supposed to be 2csc^2(2x) + cot(2x) = 3?

If so, you should replace csc(2x) with 1/sin(2x) and cot(2x) with cos(2x)/sin(2x).

find out the solutions.

Homework Equations

cosec^2 = 1+ cot^2

The Attempt at a Solution

a) cot^2x + cosec^2x = 7
cosec^2-1 + cosec^2 = 7
2cosec^2x = 8
now i thought of solving it by the difference of squares?

So csc^2(2x) = 4
Or 1/[sin^2(2x)] = 4
Can you take it from there?

couldn't solve it =/
b) totally cluesless as this one has 2 after function cot i.e cot2x =/

 

[ibysaiyan]

sorry as i am pretty newbie with latex =/ hmm i don't get it, how did you end up with = 4? and yea i got to say.. that question doesn't make sense well the way i typed makes it more complicated (looking)

 

[Mark44]

Divide both sides of the equation by 2 to get csc^2(2x) = 4.